A GEOLOGISTS SLIDE RULE. 



245 



Two are simple logarithmic scales. On the experimental rule 10 in. 

 v.-as take^a as the unit; a foot rule with inches divided to tenths then 

 permits a reading to two places and estimation to the third place of 

 decimals. 



From a table of logarithms mark off on one edge of the narrow 

 strip of the slide the lengths corresponding to the logarithms of the 

 numbers. Beginning from one end of the slide, the leng-ths correspond- 

 ing to the numbers 10, 20, 37, 122 are lO'OO, IS^Ol, 15-68, 20-86; 

 and so on for the other numbers. The points so obtained should be 

 mariied with the values of the natural numhers corresponding to them. 

 A slide of the length described gives a range from 1 to about 150. 



Run the slide into the slide way till the ends of the two are flush, 

 and engrave on the slide way a scale identical with the one on the 

 slide. 



Now pi-oceed to engrave on the other side of the slide a 

 logarithmic cosine scale. Take the end of the slide corresponding to 

 1 on the logarithmic scale as the value 10 on the cosine ?cale (that 

 is, corresponding to an angle 0°), and engrave it exactly as above 

 described, making use of the table of logarithmic cosines given in the 

 mathematical tables. Opposite each graduation put the number in 

 degrees of the corresponding angle. 



The fourth scale, engi-aved on the other edge of the slide way, 

 is one of logarithmic tangents. Take the centre point of the edge 

 as 10, (con-esponding to the angle 45°), and graduate it by means 

 -of a logarithmic tangent table, the numbers rising in the direction 

 in which those of the cosine scale fall. 



This completes the essential part of the rule. A printed descrip- 

 tion makes the manipulation appear complicated ; it is, however, quite 

 simple in practice. 



One of the commonest mathematical operations involved in 

 geological field work is the multiplication or division of numbers. This 

 can be done by means of the two logarithmic scales. If the numbers 

 are large shift the decimal point to the left in both. For multiplica- 

 tion place the 1 graduation of one scale against the value of the 

 multiplier on the other scale; then read off on this latter scale the 

 value of the product, which comes opposite the number corresponding 

 to the multiplicand on the first scale. In division, the graduations 

 corresponding to divisor and dividend are brought together, when the 

 value of the quotient can be read off opposite the 1 graduation of the 

 scale taken for the divisor. 



This method is useful in converting paces, (of a known number 

 to the chain), into chains; chains into yards; yards into metres, &c., 

 the points on the slide scale corresponding to the factors required for 

 such reductions can be marked in red. ink to save time in mani- 

 pulation. 



It is for the evaluation of dip problems, however, that the rule is 

 specially designed. In drawing a geological section from the infor- 

 mation furnished by a map, the line of section is often oblique to the 



